On the non‐singular traction‐BIE in elasticity

Abstract

AbstractThe work reported herein develops a generalized traction‐BIE formulation which involves only weakly singular integrals (in the three‐dimensional problem) or totally regular integrals (in the two‐dimensional problem). The first step deals with the terms in the Somigliana displacement identity, and then the derivatives of these terms. The only conditions required for the existence of the traction‐BIE and the related Somigliana stress identity are weak continuity of the in‐plane derivatives of the surface displacements and of the surface tractions. It is shown that the Cauchy Principal Value (CPV) interpretations so commonly used in BIE developments are unnecessary. The formulation is established not only at a smooth boundary point, but also at a corner point. The extension of the non‐singular formulation to discontinuous boundary tractions and tangential derivatives of the boundary displacements applicable to a generalized problem statement as well as the usual BEM implementations is also shown. In the demonstrated formulation, the source points are located directly at the boundary nodes and non‐conformal elements are not needed.